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Mathematics, physics and the female mind

“You’ll never succeed!” There is nothing worse to say a child about h* ability to do something. Especially, when these words come from an authoritative person, say a teacher. And more-even-especially, when this tiny phrase is said without any real motivation - for example, because of gender.

The problem is so awkwardly complex I can say very little of it in general. I will restrict my attention to a very practical aspect: to state (and possibly prove) that gender is not an impediment to mathematical success - despite stereotypes.

Just a little bit of myth-dispelling.

An enduring myth: ”Mathematics is not for girls.”

That mathematics and physics are (considered) eminently male turf is also a commonplace, reinforced by many assumptions so common among the general public about how the female mind is supposed to operate, and how its characteristics are unsuitable for something so techy-nerdy as mathematics and physics are supposed to be.

One way the “female mind” is detected may be through tests. Of the many tests existing, one pretty nice has been developed by prof. Simon Baron-Cohen, and can be found at end of his popular book “The Essential Difference”.

The book is in itself fascinating and, in my opinion, is worth a reading. It presents a (very “male”) theory of the gendered brain, and identifies two key faces of brain function, “empathizing” and “systemizing”. These two faces can be tested (and in fact are), and the two scores you obtain can be used to see whether your brain is “female”, “male” or “balanced”.

Before writing this post I submitted myself to the test, and found the following scores:

-- Systemizing: 9 (“low”)
-- Empathizing: 61 (“above average”)

So, according to prof. Baron-Cohen, I should have an “E” or “female” brain.

Society games are lovely just because you can do with friends, but in this case I admit the excitement soon decreased, as I discovered that almost all people I know, women and men, are “E” or “Balanced” types. True “S” types in my clique are something like ten - all men, but this may be incidental (the sample is too small to authorize drawing any conclusion).

(Obviously there is a bias - that’s very unfortunate, and maybe we humans have a proclivity to chose friends with whom we can easily share our feelings - that is, similar to us. Evidently, I prefer interacting with other “E” types.)

The theory of brain type strongly suggests (to us, casual readers) some kind of “path of minimal resistance”. It is tempting to imagine a type “E” brain as a sort of ideal teacher or nurse, an “S” as an engineer, a “balanced” type as, say, a lawyer or physician. This view is in part sustained by the examples of brilliant systemizing minds listed in the book, all involved professionally in “systemizing” activities.

Is this true? (Honestly, the author did not said something like this, or at least I didn’t find. His life-interest is with autism and Asperger syndromes, cases prof. Baron-Cohen relates to an extreme form of systemizing (“male”) brain. All his examples, and most of the book, are devoted to this specific point.)

So, do “we average reader” understand correctly?

I go back to the sample of my friends: allow me to select all “type E” (almost an ineffective move: I just weed out a handful of nice systemizers). Then, retain women only (another something-like-30% flies away.)

Thinking to the more-or-less-70% remaining people, you discover something interesting: many of them are involved in professions one might imagine as “very good for type S people”.

There are even spectacular cases.

Two of them are top-notch mathematicians, with tens of published papers.

One is a software developer able (I witnessed personally) to design and begin developing a complex interactive Web site while breastfeeding her baby (and finishing her assignment in four days - the site was perfectly functional).

One other is an electrical engineer doing “something” (I don’t know exactly what - it’s too complicate for me, I just know from her words it’s related with “impedance matching”.)

As I mentioned, prof. Baron-Cohen is one of the big names on autism, worldwide. And his theory is, autism is related to a form of “extreme male (systemizer) brain”.

And, I add, he’s a man.

His use (in the divulgative book and there only, as far as I understood) of term “female brain” as a synonym of “type E” may be “reductive”, a sort of projection (in the mathematical sense) of “brain femaleness” over the “other”, male subspace.

And in fact, the female mind may have characteristics and potentialities besides (and possibly “beyond”) empathizing-more-than-systemizing.

Although not a nice thing to say, for example, we have to admit the (adult) female mind is “variable with time”. Women have a cycle, spanning the whole fertile life. In some phases of cycle (during ovulation, or for some individuals a couple days before menstruation) the mind and sensorial sharpness increases.

You may find yourself in a sort of “state of grace”, literally. You are in field, and can see the damned fault you imagined in the preceding days. Or, something inside you suddenly conceives the next family of the company’s meteorological processor, plus the steps to actually construct / test / deploy / sell it. Of course, these very good days are compensated (with interests) some days later.

But you can’t honestly say you can expect a constant level of performance. Even from cycle to cycle there are subtle and not-so-subtle variations.

Does this has cognitive consequences?

Who knows…

Another possible complication to the simple model may be connected to core motivation. If you look carefully (and de-construct) the empathizing vs systemizing test, you can see it does not deal with abilities, but rather with motivation.

(This offers to me a good escape way for my shameful systemizing score: it’s all because of lack of motivation! ;-) Just as an anecdote, it took me two years to realize the neat and tidy plastic cover of my car’s engine was just a cover, and not the (horribly dirty) engine itself - mainly because I have no interest in engines, as in many other techy things inessential to my life).

Motivation may act in complex ways.

For example: a “type E” person is doggedly motivated by relating with someone. What this “someone” is? Another person? Anything else? A system?

For some of my friends, this is exactly what happens. They relate mostly with people, but also with other things (most often living beings, but not rarely entire systems).

They are, and remain, “type E”. But, they can “systemize”, their way.

Our motivation may also be rooted in something more mundane: if you get a degree in applied mathematics and you find yourself catapulted into an industrial automation company (as happened to a friend of mine and myself), then your interest in understanding how a supervisory control and data acquisition system functions grows. Guaranteed.

Whatever the cause at the root of our motivation, it is this latter's power to make us daring or not.

My preferred analogy is drawn form quantum physics. We are like an electron facing a potential barrier. As it, we may pass the barrier or not, and the probability of passage depends on how high the barrier threshold is, and how large the energy we have.

If this analogy is something more than an analogy, it would be possible to convince more girls to "pass the potential barrier" working on the energy - imagining the barrier threshold is much more difficult to change. Sincerely, I strongly believe in this, but I have no proof.

By the way: if convinced to cross the potential barrier, the "type E" people systemize, and in fact often very well.

Now: is there some specific way women use to “systemize”?

Web-thinking and Root-expanding

In the (extremely intriguing) book "Women's Way of Knowing", by Mary Field Belenky, Blythe McVicker Clinchy, Nancy Rule Goldberg and Jill Mattuck Tarule, the knowing-individual growth process is followed for men and women, the latter conducing to a "subjective knowledge" (knowledge assumed dependent on the (relation between observed and) observer), which can further develop into a "constructive knowledge" (knowledge as a human construction, dependent on both the observer and cultural context, and potentially modifiable).

Knowledge (of a system) deepens and widens, mostly unobserved, under the drive of a sort of primitive desire to relate. I figure this process as roots and rootlets growing in many directions, in parallel. Some die, some others become larger and more robust.

This is largely unplanned.

Its end result is a complex web, constantly reconfiguring. This natural evolution of knowledge even reflects at conscious level, as the many descriptions of "web thinking" show. (An account of this concept may be found in "The First Sex" by Helen Fisher, and bibliography).

Is "web-understanding" (would we introduce this name to designate the women-related way of systemizing) really any different than the form of systemizing introduced by prof. Baron-Cohen?

Surely, seen from outside a web of knowledge seems:
-- complex
-- potentially ambiguous (not per se bad - in fact, a possible advantage in many situations)
-- subjective (in the sense of "dependent on the observer")
-- potentially (but not necessarily) very accurate.

Webs of knowledges, by the way, demand a lot of emotional energy - you form them, only if you support them in love for a long, potentially unpredictable, time.

Large webs of knowledges may have a potentially dangerous side effect: they are difficult to communicate (and even to just visualize: I tried using programs like Axon or the like to represent complex mental webs, but the results were quite disastrous: the more you encode, the more pops up - my limit: it takes me some effort to arrive to a sensible synthesis). Translating a large web of knowledge into a communicable body requires you become a bit "linear" (and do some kind of "topological sorting" of the various elements).

As far as I have personally experienced, the "web systemizers" I know build internal representations which are as accurate maps of reality as those of "conventional systemizers".

A room on one's own (once again)

You can pass your potential barrier, if conditions are favorable.

But this is not sufficient for large webs of knowledge to form and consolidate.

Time, friendly support, self-reliance and sustained will must operate. For a very long time. An entire life, possibly.

As Virginia Woolf said, you need a room on your own.

A room in space or, in these overbusy times, time.

A safe place, real or figurate, in which securely thinking and exploring.

To carve this place out, and protect it, may be a formidable task.

Sustainable only by an enduring passion (a huge responsibility!)

I close, with a name and a little story. The name is Sophie Germain, one of the major mathematicians in 18th and early 19th centuries. Her works, struggles and findings are now commonplace, and I have nothing to add.

I just remember one thing: her candle.

She was so passionate of mathematics that, once a girl, she devoted all her free time to it, and possibly some more. Her parents worried of her health, and "in her interest" attempted to cut anything she needed to go on, beginning with paper.

Their effort (fortunately for the human race) were unsuccessful. Sophie grasped any surface on which it was in principle possible to write, used shopping lists included. And a candle, that she secretly lighted once in her room to continue her studies.

All incredible she made was rooted in no more than this. An immense, indestructible passion and curiosity.

Comments

In this case I give it, as I imagine it may be of some interest to the point.

As I stated, my systemizing score was a "9".
Out of a maximum of 80, or something like that.

Quite good, isn't it? ;-)

Allow me a bit of de-construction, however.

Of the score I got, all referred to systems of "natural" type.

The systems in the "SQ test" encompass a very broad range, from relations among numbers to banking passing through engines, and much, much more.

Obtaining a high SQ score means being likely to be attracted at all these disparate kinds of systems at once.
That is (I imagine this is the actual meanings of the test) to be attracted by systems "as systems". To derive some joy from understanding their underlying rules, breaking codes, while remaining after all detached.

I admit am not detached. I had fallen in love with various subjects (all natural and human), and developed my own quirky web of knowledge about them (all messing together in a curious way).

But, I definitely am not interested in "systems" indiscriminately (as a sort of, please forgive me the ugly term, "mental promiscuity"). Breaking a code without any "love" seems to me unrewarding - I sometimes "have" to do at work, but that's just that: work. In very rare cases, entering in contact with a system I was not "in love with" may foster some curiosity. But in the end, if allowed, I don't do.

"Knowing" is, in my experience, an intimate journey. Always. With people as with nature.
It is never something "short" you can do on demand and on command. It involves participation, and an openness to "allowing this other to change you" (it does, invariably).

The difference between "being in love with systems as systems" and loving just few resembles me the difference between "understanding" a difficult mathematics book in the sense of reading it validating all passages (a cold experience, something you do to pass an exam), and "understanding in the real sense", that is, assimilating its contents deeply, to the point you begin to foresee the "beauty" into it.

So: towards systems I am a sort of "K-strategist". In them, I invest a lot. My mental energy, emotional commitment and time are finite, so I devote to the one I really feel "pertinent" to me.

What the "SQ test" scores high resembles me a sort of "r strategist's" attitude towards material world. Very "male", and maybe at a much deeper level that prof. Baron-Cohen described in his booklet.

Why just 9 points, by the way?

Could it be incidental?

I said the test deals with systems encompassing a very broad range. But real world systems are in reality almost countless, and a complete test may not be just devisable (it would take too much volumes, so many a single life may not be sufficient to just read them casually). Clearly the SQ test is a tiny subset. Another SQ test may be formulated on a different subset, and there (by chance) my score might change - it would depend on how many of these systems are attractive to me.

To be sincere, a score like "9" describes quite accurately my general attitude, and I would not change it intentionally, by doctoring data or ironing-out some of the answers. In my life I have dealt with systems of various types, and in some cases with sufficient success to win my breadcrumb as an engineer. But frankly, would all depend entirely on me, I'd try following my inclinations along different pathways.

And what of the "EQ"? I got a high score there.

But a same kind of inherent bias may apply. There are infinite ways to empathize, and I'm not proclive to all of them.
Formulating the test in a different manner would maybe yield a very low value.

Tests are always projection of the tester designer's mind.

I also have nothing special to say of my 61 in "EQ": it matches quite well what some teachers and other people told me of myself. I'm not that sure it's a good thing (actually, some of these teachers tried, based on their judgment on me, to address me towards some care profession instead of science (and "systems")).

You also have to be careful. That's my own impression, at least. I obtained a "score above average" on a character someone (a man, in this specific case) uses (let me say it plainly) as a proxy of "femininity".

That may be fine, if you like. You may even feel honored that someone find you belong to the human species after all.

But could also (meantime) be something reductive and extremely inaccurate when evaluating a whole person.

In Junghian terms (of which I'm not an expert) prof. Baron-Cohen high score of my "EQ" looks (also) as an "Anima projection". I know well some people did the same towards me many times; I imagine you have had the same experience - being the target of the "Anima projection" of someone else, even friends, isn't nice. There are so many other things in us (often terrible, or just neutral) - and besides, projections are just "models", so often ways to stereotype someone else denying any further real contact.

So, naturally, I was drawn to the test and I scored 37 on the SQ and 63 on the EQ. What seems curious to me is that I scored higher than you on the SQ when you clearly have a much greater understanding of systems than me. But I put it down to my deep curiosity about things which does not necessarily lead to an understanding. I will read about a theory because I have a need to make sense of the world BUT doing so does not naturally lead to greater comprehension of the topic and sometimes, in fact, I am left more confused. Sometimes, I may have to read something over and over to grasp the meaning, e.g. entanglement in quantum physics.

An interesting and fun exercise that, as you state, is in the end just an exercise. Labels have a way of limiting one's perspective of another and so with any label, we take the results with a grain of salt and chalk it up to one more thing that adds to the complex beauty that make up each individual.

Are you "really so sure" I have a "much greater understanding of systems" than you? ;-)

I'm a very finicky person - I am in deep love with "some" systems (mostly off-SQ-test, by the way), but not with the idea of "system" in itself.

Well, maybe. I recently "discovered" how many things are there to explore in the field of "complex" systems - more specifically, systems composed by large numbers of very simple parts exchanging information according to some simple rule. These systems, taken as wholes, behave in a way much more rich than the sum of their part. As an immune system, a swarm, a galaxy...

The very idea that something new can form from "almost nothing" fascinates me. It looks so much as a birth-and-growth process! Something warming heart and mind together. This attracts me...

Do you too have the impression that some theories "dispel"? Many years ago I met the "theory of catastrophes", after a friend of mine (a professor of quantitative ecology) asked me to check it. I read René Thom's classical presentation many times (and, it was very hard, mainly because I lacked sufficient mathematical skill on that time), until I felt sure I understood it logically. In some way, however, on that time I did not accept it at a deep level. I can't say exactly why, but I had the impression of something disturbing was buried inside of it. Maybe, its apparently rigid determinism (at least, as I imagined on that time - some months ago I revised again the same material, and found it much less threatening, if any at all.

Other theories, on the contrary, seem on a first glance "attractive". Entanglement, as you quoted it, is one of them. State correlation between two particles "far away" suggests they may not be that far, after all. Like as if the space of physics (even the "four-dimensional" macroscopic space-time we are used to) is described by an Euclidean variety only in first approximation. As, if space is a sort of hologram. As if my "here, now" is also a little bit of "where you are, in that moment". This may be a crazy way to conceptualize entanglement, but I feel it deeply "rewarding", in some way reassuring.